[Math] Rolling a fair 6-faced die twice, what is the probability that the sum of the two rolls is 6 given that the first one is an even number

Question

Rolling a fair 6-sided die twice, what is the probability that the sum of the two rolls is exactly 6 given that the first one is an even number?

Answer 1

First die can be 2, 4, or 6. Second any roll 1-6. So the sample space is $3 \cdot 6= 18$ Only two positive outcomes: {2,4} and {4,2}.

Probability $= \frac{2}{18} = \frac{1}{9}$